{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:22Z","timestamp":1740107122905,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T00:00:00Z","timestamp":1703030400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T00:00:00Z","timestamp":1703030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771080"],"award-info":[{"award-number":["11771080"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s00373-023-02732-x","type":"journal-article","created":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T06:01:52Z","timestamp":1703052112000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Maximum 4-Vertex-Path Packing of a Cubic Graph Covers At Least Two-Thirds of Its Vertices"],"prefix":"10.1007","volume":"40","author":[{"given":"Wenying","family":"Xi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4112-0469","authenticated-orcid":false,"given":"Wensong","family":"Lin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,20]]},"reference":[{"key":"2732_CR1","volume-title":"Path Factors of a Graph. Graphs and Applications","author":"J Akiyama","year":"1984","unstructured":"Akiyama, J., Kano, M.: Path Factors of a Graph. Graphs and Applications. Wiley, New York (1984)"},{"issue":"1","key":"2732_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/jgt.3190090103","volume":"9","author":"J Akiyama","year":"1985","unstructured":"Akiyama, J., Kano, M.: Factors and factorizations of graphs\u2014a survey. J. Graph Theory 9(1), 1\u201342 (1985)","journal-title":"J. Graph Theory"},{"issue":"6","key":"2732_CR3","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/j.ipl.2016.01.007","volume":"116","author":"F Barbero","year":"2016","unstructured":"Barbero, F., Jones, G., Sheng, M., Yeo, A.: Linear-vertex kernel for the problem of packing $$r$$-stars into a graph without long induced paths. Inf. Process. Lett. 116(6), 433\u2013436 (2016)","journal-title":"Inf. Process. Lett."},{"issue":"1","key":"2732_CR4","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/s10878-012-9594-4","volume":"27","author":"H Eto","year":"2014","unstructured":"Eto, H., Guo, F., Miyano, E.: Distance-$$d$$ independent set problems for bipartite and chordal graphs. J. Combin. Optim. 27(1), 88\u201399 (2014)","journal-title":"J. Combin. Optim."},{"key":"2732_CR5","doi-asserted-by":"crossref","unstructured":"Eto, H., Ito, T., Liu, Z., Miyano, E.: Approximation algorithm for the distance-$$3$$ independent set problem on cubic graphs, WALCOM: Algorithms and Computation: 11th International Conference and Workshops, WALCOM: Hsinchu, Taiwan. Proceedings 2017, 228\u2013240 (2017)","DOI":"10.1007\/978-3-319-53925-6_18"},{"issue":"1","key":"2732_CR6","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s006070170039","volume":"66","author":"V Guruswami","year":"2001","unstructured":"Guruswami, V., Rangan, C.P., Chang, M.S., Chang, G.J., Wong, C.K.: The $$K_r$$-packing problem. Computing 66(1), 79\u201389 (2001)","journal-title":"Computing"},{"issue":"1","key":"2732_CR7","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0012-365X(84)90150-X","volume":"49","author":"P Hell","year":"1984","unstructured":"Hell, P., Kirkpatrick, D.G.: Packing by cliques and by finite families of graphs. Discrete Math. 49(1), 45\u201359 (1984)","journal-title":"Discrete Math."},{"issue":"2","key":"2732_CR8","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1137\/0607024","volume":"7","author":"P Hell","year":"1986","unstructured":"Hell, P., Kirkpatrick, D.G.: Packing by complete bipartite graphs. SIAM J. Algorithm Discrete Math. 7(2), 199\u2013209 (1986)","journal-title":"SIAM J. Algorithm Discrete Math."},{"key":"2732_CR9","doi-asserted-by":"crossref","unstructured":"Hell, P., Kirkpatrick, D.G., Kratochv\u00edl, J., Kr\u0306\u00edz\u0306, I.: On restricted two-factors. SIAM J. Discrete Math. 1(4):471\u2013484 (1998)","DOI":"10.1137\/0401046"},{"issue":"1","key":"2732_CR10","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1137\/0402008","volume":"2","author":"C Hurkens","year":"1989","unstructured":"Hurkens, C., Schrijver, A.: On the size of systems of sets every $$t$$ of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM J. Discrete Math. 2(1), 68\u201372 (1989)","journal-title":"SIAM J. Discrete Math."},{"issue":"4","key":"2732_CR11","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1002\/1097-0118(200104)36:4<175::AID-JGT1005>3.0.CO;2-T","volume":"36","author":"A Kaneko","year":"2001","unstructured":"Kaneko, A., Kelmans, A., Nishimura, T.: On packing $$3$$-vertex paths in a graph. J. Graph Theory 36(4), 175\u2013197 (2001)","journal-title":"J. Graph Theory"},{"issue":"2","key":"2732_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0095-8956(03)00027-3","volume":"88","author":"A Kaneko","year":"2003","unstructured":"Kaneko, A.: A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two. J. Combin. Theory Ser. B 88(2), 195\u2013218 (2003)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"3","key":"2732_CR13","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1002\/jgt.10022","volume":"39","author":"K Kawarabayashi","year":"2002","unstructured":"Kawarabayashi, K., Matsuda, H., Oda, Y., Ota, K.: Path factors in cubic graphs. J. Graph Theory 39(3), 188\u2013193 (2002)","journal-title":"J. Graph Theory"},{"key":"2732_CR14","unstructured":"Kelmans, A.: Packing $$P_k$$ in a cubic graph is NP-hard for $$k\\ge 3$$, manuscript (2001)"},{"issue":"1","key":"2732_CR15","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1002\/jgt.10136","volume":"45","author":"A Kelamns","year":"2003","unstructured":"Kelamns, A., Mubayi, D.: How many disjoint $$2$$-edge paths must a cubic graph have? J. Graph Theory 45(1), 57\u201379 (2003)","journal-title":"J. Graph Theory"},{"issue":"2\u20133","key":"2732_CR16","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.dam.2010.05.001","volume":"159","author":"A Kelmans","year":"2011","unstructured":"Kelmans, A.: Packing $$3$$-vertex paths in claw-free graphs and related topics. Discrete Appl. Math. 159(2\u20133), 112\u2013127 (2011)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"2732_CR17","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1137\/0212040","volume":"12","author":"DG Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, D.G., Hell, P.: On the complexity of general graph factor problems. SIAM J. Comput. 12(3), 601\u2013609 (1983)","journal-title":"SIAM J. Comput."},{"key":"2732_CR18","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1007\/11752578_121","volume":"3911","author":"A Kosowski","year":"2005","unstructured":"Kosowski, A., Malafiejski, M., \u017byli\u0144ski, P.: Parallel processing subsystems with redundancy in a distributed environment. Int. Conf. Parallel Process. Appl. Math. 3911, 1002\u20131009 (2005)","journal-title":"Int. Conf. Parallel Process. Appl. Math."},{"key":"2732_CR19","first-page":"1","volume":"89","author":"A Kosowski","year":"2008","unstructured":"Kosowski, A., \u017byli\u0144ski, P.: Packing three-vertex paths in $$2$$-connected cubic graphs. Ars Combin. 89, 1\u201319 (2008)","journal-title":"Ars Combin."},{"issue":"5","key":"2732_CR20","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s00373-008-0807-7","volume":"24","author":"A Kosowski","year":"2008","unstructured":"Kosowski, A., Malafiejski, M., \u017byli\u0144ski, P.: Tighter bounds on the size of a maximum $$P_3$$-matching in a cubic graph. Graphs Combin. 24(5), 461\u2013468 (2008)","journal-title":"Graphs Combin."},{"key":"2732_CR21","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1016\/j.orl.2006.12.004","volume":"35","author":"J Monnot","year":"2007","unstructured":"Monnot, J., Toulouse, S.: The path partition problem and related problems in bipartite graphs. Oper. Res. Lett. 35, 677\u2013684 (2007)","journal-title":"Oper. Res. Lett."},{"key":"2732_CR22","first-page":"195","volume":"92","author":"AA Mutairi","year":"2015","unstructured":"Mutairi, A.A., Ali, B., Manuel, P.: Packing in carbon nanotubes. J. Combin. Math. Combin. Comput. 92, 195\u2013206 (2015)","journal-title":"J. Combin. Math. Combin. Comput."},{"issue":"3","key":"2732_CR23","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1145\/322326.322328","volume":"29","author":"K Takamizawa","year":"1982","unstructured":"Takamizawa, K., Nishizeki, T., Saito, N.: Linear-time computability of combinatorial problems on series-parallel graphs. J. Assoc. Comput. Mach. 29(3), 623\u2013641 (1982)","journal-title":"J. Assoc. Comput. Mach."},{"issue":"2","key":"2732_CR24","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1002\/jgt.3190180207","volume":"18","author":"H Wang","year":"1994","unstructured":"Wang, H.: Path factors of bipartite graphs. J. Graph Theory 18(2), 161\u2013167 (1994)","journal-title":"J. Graph Theory"},{"issue":"3","key":"2732_CR25","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1007\/s10878-021-00708-2","volume":"41","author":"W Xi","year":"2021","unstructured":"Xi, W., Lin, W.: On maximum $$P_3$$-packing in claw-free subcubic graphs. J. Combin. Optim. 41(3), 694\u2013709 (2021)","journal-title":"J. Combin. Optim."},{"key":"2732_CR26","doi-asserted-by":"crossref","unstructured":"Xi, W., Lin, W.: The maximum $$3$$-star packing problem in claw-free cubic graphs (2022)","DOI":"10.1007\/s10878-021-00708-2"},{"issue":"2","key":"2732_CR27","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1017\/S0004972721000952","volume":"106","author":"S Zhou","year":"2022","unstructured":"Zhou, S., Wu, J., Xu, Y.: Toughness, isolated toughness and path factors in graphs. Bull. Aust. Math. Soc. 106(2), 195\u2013202 (2022)","journal-title":"Bull. Aust. Math. Soc."},{"issue":"8","key":"2732_CR28","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1007\/s10114-020-9224-5","volume":"36","author":"S Zhou","year":"2020","unstructured":"Zhou, S., Sun, Z.: Some existence theorems on path factors with given properties in graphs. Acta Math. Sin. Engl. Ser. 36(8), 917\u2013928 (2020)","journal-title":"Acta Math. Sin. Engl. Ser."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-023-02732-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-023-02732-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-023-02732-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T18:05:00Z","timestamp":1711821900000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-023-02732-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,20]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["2732"],"URL":"https:\/\/doi.org\/10.1007\/s00373-023-02732-x","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2023,12,20]]},"assertion":[{"value":"19 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declares that there is no conflict of interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"5"}}